Weighted Norm Inequalities for Geometric Fractional Maximal Operators.
Weighted norm inequalities for maximal functions and singular integrals
Weighted norm inequalities for maximal functions from the Muckenhoupt conditions.
For some pairs of weight functions u, v which satisfy the well-known Muckenhoupt conditions, we derive the boundedness of the maximal fractional operator Ms (0 ≤ s < n) from Lvp to Luq with q < p.
Weighted norm inequalities for multilinear fractional operators on Morrey spaces
A weighted theory describing Morrey boundedness of fractional integral operators and fractional maximal operators is developed. A new class of weights adapted to Morrey spaces is proposed and a passage to the multilinear cases is covered.
Weighted norm inequalities for Riesz potentials and fractional maximal functions in mixed norm Lebesgue spaces
Weighted norm inequalities for singular integral operators satisfying a variant of Hörmander's condition
In this paper we establish weighted norm inequalities for singular integral operators with kernel satisfying a variant of the classical Hörmander's condition.
Weighted norm inequalities for the geometric maximal operator.
Weighted norm inequalities for vector-valued singular integrals on homogeneous spaces
Let X be a homogeneous space and let E be a UMD Banach space with a normalized unconditional basis . Given an operator T from to L¹(X), we consider the vector-valued extension T̃ of T given by . We prove a weighted integral inequality for the vector-valued extension of the Hardy-Littlewood maximal operator and a weighted Fefferman-Stein inequality between the vector-valued extensions of the Hardy-Littlewood and the sharp maximal operators, in the context of Orlicz spaces. We give sufficient...
Weighted norm inequalities relating the and the area functions
Weighted norm inequality for the Poisson integral on the sphere.
Weighted Orlicz space integral inequalities for the Hardy-Littlewood maximal operator
Necessary and sufficient conditions are given for the Hardy-Littlewood maximal operator to be bounded on a weighted Orlicz space when the complementary Young function satisfies . Such a growth condition is shown to be necessary for any weighted integral inequality to occur. Weak-type conditions are also investigated.
Weighted reverse weak type inequality for general maximal functions.
Weighted sharp maximal function inequalities and boundedness of a linear operator associated to a singular integral operator with non-smooth kernel
We establish weighted sharp maximal function inequalities for a linear operator associated to a singular integral operator with non-smooth kernel. As an application, we obtain the boundedness of a commutator on weighted Lebesgue spaces.
Weighted Sobolev-Lieb-Thirring inequalities.
We give a weighted version of the Sobolev-Lieb-Thirring inequality for suborthonormal functions. In the proof of our result we use phi-transform of Frazier-Jawerth.
Weighted two-parameter Bergman space inequalities.
Weighted variable integral inequalities for the maximal operator on non-increasing functions
Let be the Ariõ-Muckenhoupt weight class which controls the weighted -norm inequalities for the Hardy operator on non-increasing functions. We replace the constant p by a function p(x) and examine the associated -norm inequalities of the Hardy operator.
Weighted weak type (1,1) estimates for singular integrals and Littlewood-Paley functions
We prove some weighted weak type (1,1) inequalities for certain singular integrals and Littlewood-Paley functions.
Weighted weak type inequalities for certain maximal functions
We give an A_p type characterization for the pairs of weights (w,v) for which the maximal operator Mf(y) = sup 1/(b-a) ʃ_a^b |f(x)|dx, where the supremum is taken over all intervals [a,b] such that 0 ≤ a ≤ y ≤ b/ψ(b-a), is of weak type (p,p) with weights (w,v). Here ψ is a nonincreasing function such that ψ(0) = 1 and ψ(∞) = 0.
Zygmund's program: some partial solutions
We present a simple criterion to decide whether the maximal function associated with a translation invariant basis of multidimensional intervals satisfies a weak type estimate. This allows us to complete Zygmund’s program of the description of the translation invariant bases of multidimensional intervals in the particular case of products of two cubic intervals. As a conjecture, we suggest a more precise version of Zygmund’s program.
-central BMO estimates for commutators of -dimensional Hardy operators.